The veto threat could buck up Democrats looking to kill the bill in an effort to push Republicans to pass a more generous version.

"Republicans have had more than a year to comprehensively fix the Nation's broken immigration system, but instead of working toward a real, lasting solution, Republicans released patchwork legislation that will only put more arbitrary and unrealistic demands on an already broken system," the White House's Office of Management and Budget said in a Statement of Administration Policy. "H.R. 5230 could make the situation worse, not better. By setting arbitrary timelines for the processing of cases, this bill could create backlogs that could ultimately shift resources away from priority public safety goals, like deporting known criminals," the statement said. "This bill will undercut due process for vulnerable children which could result in their removal to life threatening situations in foreign countries. In addition, the limited resources provided in H.R. 5230 are not designated as emergency, but rather come at the expense of other Government functions."

The administration also ripped the bill for failing to include money for wildfires, or for Israel's Iron Dome missile defense system.

The veto threat was of the milder "advisers would recommend" variety, however.

The White House's threat comes as Speaker John A. Boehner, R-Ohio, tries to whip votes for the bill amid strong Democratic opposition and skepticism among some conservative Republicans.